If an object of mass M is suspended from the bottom of the rope in Problem 59,

Question:

If an object of mass M is suspended from the bottom of the rope in Problem 59,
(a) Show that the time interval for a transverse pulse to travel the length of the rope is
Δt = 2 √L/ mg (√M + m ─√M)
What If?
(b) Show that this reduces to the result of Problem 59 when M = 0.
(c) Show that for m << M, the expression in part (a) reduces to Δt = √mL/ Mg